My banking app works just fine on GrapheneOS, and it’s required no tinkering to get it working the way I want. I can’t speak for smart watches unfortunately, but I’d still recommend a Pixel with GrapheneOS if you really care about privacy. If you really don’t want to go with GrapheneOS, I’d still recommend Android. Apple may be marketing towards privacy friendly, but Android still has better FOSS options, which is better than blindly trusting Apple.
I use the Shield Pro, and it works great for streaming Steam games. I’ve never used moonlight/sunshine, but Steam Link has worked flawlessly for me, as well as xbox controllers, PS4 controllers, and Switch controllers and their knockoffs. My only gripe is it only has the HDMI port for 4k/60hz (HDMI 2.1? Can’t remember the number) and can’t stream the 4k/120hz my TV can handle.